Vladimir Aleksandrovich Fock was one of the group of brilliant physics theoreticians whose work built the magnificent edifice of the quantum theory.

From the vast subject of the quantum theory the author has chosen material limited in two respects. First, the book considers none but the main principles and simplest applications of quantum mechanics, It concerns itself exclusively with the one-body problem. It does not deal with the many-body problem or the Pauli exclusion principle, basic to that problem. Second, the author has sought to confine himself to that part of the theory that is’ considered proved, that is, quantum mechanics proper. He has not examined quantum electrodynamics since this theory has yet to be fully elaborated.

The author’s main purpose is to introduce the reader to a new set of ideas differing greatly from the classical theory. He has endeavoured to avoid using images from the classical theory as being inapplicable to quantum physics. Rather, he has attempted to familiarize the reader with the basic concepts underlying a quantum description of the states of atomic systems.

The second edition of this book, unlike the first, devotes a separate chapter to the nonrelativistic theory of the electron spin (Pauli’s theory of the electron) and contains a chapter on the many-electron problem of quantum mechanics. In addition, some of the author’s findings have been incorporated as separate sections. Otherwise, the subject matter of the book (both the mathematical theory and its physical interpretation) remains the same, except for certain new formulations of an epistemological character (the concepts of relativity with respect to the means of observation and of potential possibility), which has necessitated changing the expression “the statistical interpretation of quantum mechanics” to “the probabilistic interpretation”. The new formulations are more precise than the previous ones.

The title of the book speaks for itself. The word “fundamentals” can be understood as “basic principles” or as “introductory facts”.

About the author:
Vladimir Aleksandrovich Fock was one of the group of brilliant physics theoreticians whose work built the magnificent edifice of the quantum theory. A contemporary of Niels Bohr, Lev landau, Werner Heisenberg, and Paul Dirac, he contributed much to practically all fields of theoretical and mathematical physics. His books The Theory of Space, Time and Gravitation, and Electromagnetic Diffraction and Propagation Problems have been translated into English (Pergamon Press). In 1936 Vladimir Fock merited the Mendeleev prize for his work in quantum theory of atoms, in 1946 the State prize for his work in the propagation of radio waves, and in 1960 the Lenin prize for his work in quantum field theory. In 1932 Vladimir Fock became a Corresponding Member of the USSR Academy of Sciences and in 1939 a Full Member.

The book was translated from the Russian by Eugene Yankovsky and was published by Mir in 1978, 1982 and 1986. The present scan is from the 1986 print.

Chapter III. Radiation, the theory of dispersion, and the law of decay 137

1. Classical formulas 137
2. Charge density and current density 139
3. Frequencies and intensities 143
4. Intensities in a continuous spectrum 146
5. Perturbation of an atom by a light wave 148
6. The dispersion formula 150
7. Penetration of a potential barrier by a particle 153
8. The law of decay of a quasi-stationary state 156

1. General remarks 188
2. The radial equation for the hydrogen atom. Atomic units 188
3. Solution of an auxiliary problem 190
4. Some properties of generalized Laguerre polynomials 193
5. Eigenvalues and eigenfunctions of the auxiliary problem 197
6. Energy levels and radial functions for the discrete hydrogen spectrum 198
7. Solution of the differential equation for the continuous spectrum in the form of a definite integral 201
8. Derivation of the asymptotic expression 204
9. Radial functions for the continuous hydrogen spectrum 207
10. Intensities in the hydrogen spectrum 211
11. The Stark effect. General remarks 215
12. The Schrodinger equation in parabolic coordinates 216
13. Splitting of energy levels in an electric field 219
14. Scattering of a.-particles. Statement of the problem 221
15. Solution of equations 223
16. The Rutherford scattering law 225
17. The virial theorem in classical and in quantum mechanics 226
18. Some remarks concerning the superposition principle and the probabilistic interpretation of the wave function 229
PART III PAULl’S THEORY OF THE ELECTRON
1. The electron angular momentum 232
2. The operators of total angular momentum in spherical coordinates 236
3. Spherical harmonics with spin 239
4. Some properties of spherical harmonics with spin 243
5. The Pauli wave equation 245
6. Operator P in spherical and cylindrical coordinates and its relation to .A 248
7. An electron in a magnetic field 254
PART IV THE MANY-ELECTRON PROBLEM OF QUANTUM MECHANICS
AND THE STRUCTURE OF ATOMS
1. Symmetry properties of the wave function 257
2. The Hamiltonian and its symmetry 262
3. The self-consistent field method 263
4. The equation for the valence electron and the operator of quantum
exchange 269
5. The self-consistent field method in the theory of atoms 271
6. The symmetry of the Hamiltonian of a hydrogen like atom 276

PART V DIRAC’S THEORY OF THE ELECTRON

Chapter I. The Dirac equation 281
1. Quantum mechanics and the theory of relativity 281
2. Classical equations of motion 281
3. Derivation of the wave equation 283
4. The Dirac matrices 284
5. The Dirac equation for a free electron 288
6. Lorentz transformations 291
7. Form of matrix S for spatial rotations of axes and for Lorentz transformations 293
8. Current density 297
9. The Dirac equation in the case of a field. Equations of motion 298
10. Angular momentum and the spin vector in Dirac’s theory 301
11. The kinetic energy of an electron 304
12. The second intrinsic degree of freedom of the electron 305
13. Second-order equations 308

9 Responses to Fock – Fundamentals of Quantum Mechanics

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